Question: Multiply the following complex numbers: $({3-3i}) \cdot ({5-5i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({3-3i}) \cdot ({5-5i}) = $ $ ({3} \cdot {5}) + ({3} \cdot {-5}i) + ({-3}i \cdot {5}) + ({-3}i \cdot {-5}i) $ Then simplify the terms: $ (15) + (-15i) + (-15i) + (15 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 15 + (-15 - 15)i + 15i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 15 + (-15 - 15)i - 15 $ The result is simplified: $ (15 - 15) + (-30i) = -30i $